NeRF

We present a method that achieves state-of-the-art results for synthesizing novel views of complex scenes by optimizing an underlying continuous volumetric scene function using a sparse set of input views. Our algorithm represents a scene using a fully connected (nonconvolutional) deep network, whose input is a single continuous 5D coordinate (spatial location ( x , y , z ) and viewing direction ( θ, ϕ )) and whose output is the volume density and view-dependent emitted radiance at that spatial location. We synthesize views by querying 5D coordinates along camera rays and use classic volume rendering techniques to project the output colors and densities into an image. Because volume rendering is naturally differentiable, the only input required to optimize our representation is a set of images with known camera poses. We describe how to effectively optimize neural radiance fields to render photorealistic novel views of scenes with complicated geometry and appearance, and demonstrate results that outperform prior work on neural rendering and view synthesis.

On modelling of thermodynamic interaction of particles suspended in two-dimensional medium

Analytical description of temperature distribution in a medium with foreign inclusions is difficult due to the complicated geometry of the problem, so asymptotic and numerical methods are usually used to model thermodynamic processes in heterogeneous media. To be convinced in convergence of these methods the authors consider model problem about two identical round particles in infinite planar medium with temperature gradient which is constant at infinity. Authors refine multipole expansion of the solution obtained earlier by continuing it up to higher powers of small parameter, that is nondimensional radius of thermodynamically interacting particles. Numerical approach to the problem using ANSYS software is described; in particular, appropriate choice of approximate boundary conditions is discussed. Authors ascertain that replacement of infinite medium by finite-sized domain is important source of error in FEM. To find domain boundaries in multiple inclusions’ problem the authors develop “fictituous particle” method; according to it the cloud of particles far from the center of the cloud acts approximately as a single equivalent particle of greater size and so may be replaced by it. Basing on particular quantitative data the dependence of domain size that provides acceptable accuracy on thermal conductivities of medium and of particles is explored. Authors establish series of numerical experiments confirming convergence of multipole expansions method and FEM as well; proximity of their results is illustrated, too.

A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes

The existence and uniqueness of the discrete solutions of a porous medium equation with diffusion are demonstrated. The Cauchy problem contains a fractional Laplacian and it is equivalent to the extension formulation in the sense of trace and harmonic extension operators. By using the generalized finite difference method, we obtain the convergence of the numerical solution to the classical/theoretical solution of the equation for nonnegative initial data sufficiently smooth and bounded. This procedure allows us to use meshes with complicated geometry (more realistic) or with an irregular distribution of nodes (providing more accurate solutions where needed). Some numerical results are presented in arbitrary irregular meshes to illustrate the potential of the method.

Numerical Exploration via Least Squares Estimation on Three Dimensional MHD Yield Exhibiting Nanofluid Model with Porous Stretching Boundaries

The numerical study of a three-dimensional magneto-hydrodynamic (MHD) Casson nano-fluid with porous and stretchy boundaries is the focus of this paper. Radiation impacts are also supposed. A feasible similarity variable may convert a verbalized set of nonlinear “partial” differential equations (PDEs) into a system of nonlinear “ordinary” differential equations (ODEs). To investigate the solutions of the resulting dimensionless model, the least-square method is suggested and extended. Maple code is created for the expanded technique of determining model behaviour. Several simulations were run, and graphs were used to provide a thorough explanation of the important parameters on velocities, skin friction, local Nusselt number, and temperature. The comparison study attests that the suggested method is well-matched, trustworthy, and accurate for investigating the governing model’s answers. This method may be expanded to solve additional physical issues with complicated geometry.

Modeling Complex Systems by Structural Invariants Approach

When modeling complex systems, we usually encounter the following difficulties: partiality, large amount of data, and uncertainty of conclusions. It can be said that none of the known approaches solves these difficulties perfectly, especially in cases where we expect emergences in the complex system. The most common is the physical approach, sometimes reinforced by statistical procedures. The physical approach to modeling leads to a complicated description of phenomena associated with a relatively simple geometry. If we assume emergences in the complex system, the physical approach is not appropriate at all. In this article, we apply the approach of structural invariants, which has the opposite properties: a simple description of phenomena associated with a more complicated geometry (in our case pregeometry). It does not require as much data and the calculations are simple. The price paid for the apparent simplicity is a qualitative interpretation of the results, which carries a special type of uncertainty. Attention is mainly focused (in this article) on the invariant matroid and bases of matroid (M, BM) in combination with the Ramsey graph theory. In addition, this article introduces a calculus that describes the emergent phenomenon using two quantities—the power of the emergent phenomenon and the complexity of the structure that is associated with this phenomenon. The developed method is used in the paper for modeling and detecting emergent situations in cases of water floods, traffic jams, and phase transition in chemistry.

Influence of different materials used for 3D printing in miniature speaker enclosure development

Additive manufacturing techniques are commonly used in industry and mechanical prototyping. The past years brought rapid growth in this technology development, also in the speaker cabinets manufacturing industry. We observe numerous DIY projects on the market based on the 3D printed cabinet parts; however, this technology also offers novel options that should be investigated and documented. In the current state of the art, the basic properties and construction aspects for speaker acoustic performance is not provided as the 3d printing technique is usually treated as the tool for other projects' development. This paper will provide a detailed comparison of the most common 3D printing materials used in FDM techno9logy, such as PLA, TPE, PET-G, and others with different mechanical properties. Example enclosure for a loudspeaker of 37 mm diameter will be printed in different shapes and compared for frequency and sensitivity differences. The results will be discussed, investigating the possible use of different than traditional rigid plastic enclosures and new options using complicated geometry shapes possibly to manufacture with 3D printing techniques.

Aerodynamic Fields inside S-Shaped Baffled-Channel Air-Heat Exchangers

A numerical study of an especial heat exchanger (HE) equipped with complicated geometry baffles was performed in this research study. This shell-and-tube HE could be applied in various engineering applications like solar collectors. It can be acknowledged that generating longitudinal vortices in the flow results in enhancing the turbulent convective heat transfer. In order to generate these vortices, S-shaped baffles can be applied. It should be noted that computational analysis of shell-and-tube HEs is considered a challenging task due to these vortices. So, in this study, a commercial CFD software has been used for solving the problem and important equation and numerical approach used in the simulation have been explained. The aerodynamic aspect with respect to stream function, mean, axial, and transverse velocities, dynamic pressure, turbulent dissipation rate, turbulence kinetic energy, turbulent viscosity, and turbulence intensity fields was included in this research. This study reports many physical phenomena, such as the turbulence, instability, flow separation, and the appearance of reverse secondary currents. The average speed changed in different areas, where it is low next to the baffles. Velocity amounts are paramount around the upper channel’s wall, starting from the upper left side of the last baffle to the exit. This increase in velocity can be justified by a reduction in flow area and pressure augmentation.

3D B-Rep meshing for real-time data-based geometric parametric analysis

This paper presents an effective framework to automatically construct 3D quadrilateral meshes of complicated geometry and arbitrary topology adapted for parametric studies. The input is a triangulation of the solid 3D model’s boundary provided from B-Rep CAD models or scanned geometry. The triangulated mesh is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. This workflow includes an integration of a geometry-feature-aware pants-to-cuboids decomposition algorithm. This set of cuboids perfectly replicates the input surface topology. Using aligned global parameterization, patches are re-positioned on the surface in a way to achieve low overall distortion, and alignment to principal curvature directions and sharp features. Based on the cuboid decomposition and global parameterization, a 3D quadrilateral mesh is extracted. For different parametric instances with the same topology but different geometries, the MEG-IsoQuad method allows to have the same representation: isotopological meshes holding the same connectivity where each point on a mesh has an analogous one into all other meshes. Faithful 3D numerical charts of parametric geometries are then built using standard data-based techniques. Geometries are then evaluated in real-time. The efficiency and the robustness of the proposed approach are illustrated through a few parametric examples.